Question 5 5 pts The solution of the wave equation to = cz a us with c = 1 and the corresponding to the initial deflecti

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Question 5 5 Pts The Solution Of The Wave Equation To Cz A Us With C 1 And The Corresponding To The Initial Deflecti 1 (84.63 KiB) Viewed 97 times

Question 5 5 pts The solution of the wave equation to = cz a us with c = 1 and the corresponding to the initial deflection f (x) = sin(24) and initial velocity zero (g(x) = 0), with L = a cm, and satisfying the boundary conditions u(0, 1) = 0 and u(L, 1) = 0 for all t > 0. Hint: You have to find the following: (1) dx = 14 (2) A= So f(x) sin("** )dx; n = 1,2,3,... ci so-8(x) sin("** )dx; n = 1, 2, 3,... (4) lim->2 = x/4. 2-4 (5) The solution is u(x, t) = = sin("** ) [A, cos(An 1) + B, sin(An 1)] (3) B. sin(n) Ou(x, t) = cos(t) sin(x) 8 16 24 (X, 1) = COS(2.) sin(2x) + 3л 15x cos(41) sin(4x) + cos(61) sin(6x) + ... 35 8 (X, 1) = cos(21) sin(2x) - 3x 16 24 -Cos(41) sin(4x) + -cos(61) sin(6x) - ... 15x 35л Ou(x, t) = cos(2t) sin(2x)